Tsitsipas broke the ninth-seeded Serb early in the third set and held serve from there to reach his first career ATP World Tour Masters 1000 quarter-final.
"Losing in this kind of tournament, it's not something I don't care about", Djokovic said.
Nadal came from a mini-break down in the tiebreaker and secured victory on his second match point. "I was fearless. I played exactly how I had to play at that moment".
Holding his nerve, Tsitsipas hit a stunning backhand down the line to break serve in the second game of the third set - and never looked back.
In the tiebreaker, Zverev won a 20-shot rally to get his first match point at 6-5 but Tsitsipas poured on the pressure from the baseline and tied it. Tsitsipas saved another match point before converting his fifth set point at 13-11 when Zverev sprayed a return wide.
"I thought it went really well out there", said Polansky, who's never made it past the second round of a Rogers Cup.
"Of course I was not at 100 percent today", Nadal, 32, told reporters.
"I think it's quite an interesting experience for both of us and refreshing at times because we see each other mostly across the net", Djokovic added. "Just happy to be in the quarterfinals".
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Tsitsipas is next due to play defending champion and second seed Alexander Zverev for a place in the semi-finals after the German comfortably dispatched Daniil Medvedev 6-3, 6-2 in just 52 minutes.
Sixth seed Marin Cilic awaits in the quarter-finals following his speedy defeat of Argentina's Diego Schwartzman 6-3 6-2.
Nadal, playing for the first time since a five-set loss to Djokovic in the Wimbledon semifinals, topped France's Benoit Paire 6-2, 6-3 at night after a series of rain delays.
"I feel physically pretty well".
"I'm happy to see Stan playing well again".
South Africa's Anderson, who Djokovic beat in this year's Wimbledon final, saw off Belarus' Ilya Ivashka 7-5 6-3. Russian Karen Khachanov eliminated American John Isner 7-6 (7-5), 7-6 (7-1) in match that featured no service breaks.
Del Potro, who had a bye in the first round, was set to play Robin Haase of the Netherlands on Wednesday.